Monte Carlo Investigation of Ising Nanotubes and Nanostrips

Monte Carlo simulations of the magnetization temperature dependence in $D\times L$ nanotubes (periodic lateral boundary conditions) and nanostrips (free lateral boundary conditions) with $D$=8, 16, 32, 64$\ll L\longrightarrow 5000$ have been performed. The apparent critical temperature was determinated using the Binder Cumulant method (crossing of data for $D\times L$ with data for $D\times 2L)$ and it was found to be $T_C=0$ for small $D$ values $(D<D^{\ast })$, as it might have been expected.